Grade 9 Math Review - Functions and Linear Equations

A collection of vocabulary flashcards covering the properties of functions, domain and range, linear equations, slope, and line relationships based on Grade 9 mathematics review notes.

Relation as a Function

A relation where there are no repeated values of the $x$ coordinate.

Domain

The set of all values of the $x$ coordinate, such as $\text{-2, 0, 3, and 5}$ in the relation $\text{(-2, 4), (0, 1), (3, 4), (5, 7)}$.

Range

The set of all values of the $y$ coordinate, such as $\text{4, 1, 4, and 7}$ in the relation $\text{(-2, 4), (0, 1), (3, 4), (5, 7)}$.

Independent Variable

The variable in a model, such as $n$ in the cost equation $C = 35n$, that determines the value of the dependent variable.

Slope-Intercept Form

The form of a linear equation $y = mx + b$, where $m$ is the slope and $b$ is the $y$ intercept.

Zero of a Function

The value of $x$ when the function is equated to zero, such as in $f(x) = 2x - 10$ where the zero is $x = 5$.

Slope ($m$)

The ratio of the change in $y$ over the change in $x$, calculated as $m = \frac{y_2 - y_1}{x_2 - x_1}$.

Linear Function

A function where the highest exponent of the variable is $1$ and the variable is not located in the denominator.

Negative Slope Behavior

The characteristic of a linear function graph that decreases in value as it moves from left to right.

$x$ intercept

The point where a graph crosses the $x$ axis, determined by setting $y = 0$ and solving for $x$.

Common Difference

A constant difference between consecutive $y$ values in a table that indicates the relationship represents a linear function.

Rise and Run

The vertical and horizontal movement from the $y$ intercept used to locate another point on a line based on the slope.

Parallel Lines

Two distinct non-vertical lines that possess equal slopes.

Perpendicular Lines

Non-vertical lines that intersect such that the product of their slopes is $-1$.

Negative Reciprocal

The type of slope a line must have to be perpendicular to another, such as $-\frac{3}{2}$ for a line with a slope of $\frac{2}{3}$.

Coplanar

The condition of being in the same plane; parallel lines must be coplanar to distinguish them from skew lines, which do not intersect but are not parallel.